Elliptic curve isogeny class 4800.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-4800.1-b
• Conductor: 4800.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 4800.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 4800.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4800.1-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( 0\bigr] \)
4800.1-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -16 a + 16\) , \( -16\bigr] \)
4800.1-b3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -136 a + 136\) , \( 560\bigr] \)
4800.1-b4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -216 a + 216\) , \( -1296\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph